You know the drill.
They would probably talk each other to death.
They’d join forces, and benevolently rule the universe, ushering in an age of Enlightenment.
Until ponn farr, and then it’d be ON, baby.
I gotta go with the Jedi. Pardon my ignorance, but I can’t recall the Vulcans as being excellent fighters. The Vulcan mind-meld and the Vulcan nerve pinch require physical contact and I doubt any Jedi will let them get that close.
If we’re talking average Vulcan vs. average Jedi, I have to give it to the Jedi. Even learner Jedi can pretty much do as much and more mentally wise than most Vulcans. Vulcans do have stronger-than-human strength, IIRC, but then so do Jedi, who also have the edge in agility. Plus, there’s lightsabers.
If we’re talking fully trained Vulcan vs. full trained Jedi, Jedi wins. The Jedi can’t affect the Vulcan mentally, but they wouldn’t need to - quick burst of force lightning and it’s green ham for tea.
Vulcans are excellent warriors, but reluctant to exercise their abilities, and far stronger than humans; Kirk with a crowbar had the hardest time trying to fight off Spock with his bare hands. Also they had some esoteric techniques; there may be no Vulcan death-grip, but Spock’s father Sarek was in the frame for murder in Journey to Babel after a burly guy was found with his neck snapped clean. Spock confirmed that Sarek knew the tal-shaya technique and was plenty capable of applying it, despite being over a hundred (middle-aged in Vulcan terms) and in a sedentary occupation.
However, although you can take it for granted that nothing intended for use on “weak-minded fools” would stand a prayer against Vulcans, unless a phaser beats a light-sabre the Vulcans are on a hiding to nothing. Force lightning can probably be discounted, but even Light-Siders could and did use telekinesis, and Vulcans have no answer to that either. So regrettably my favourite Trek aliens appear to be busted.
On the other hand, if there is even theoretically possible technology to beat a light-sabre, you can count on Spock to deliver the goods. Or a way to short-circuit midi-chlorians, for that matter. Or a way to synthesise midi-chlorians and even the sides up (cf. Plato’s Stepchildren.) So matters may not be quite as cut and dried as all that. (Sorry. Midi-chlorians are canon now. I don’t like it any more than you do, but we’re stuck with it.)
The real question is whether Kirk had a crowbar and a torn shirt.
Yeah, but Spock was angry, which leads to hate, which leads to suffering.
A dark-side Vulcan…that’d kick ass. Especially with a beard.
…Especially if he was prepared.
“Obi Wan, your agonizer, please.”
In the evil Trekverse, the Vulcans make the Jedi suffer by destroying a planet.
Unfortunately, Force lightening is a Sith power-no true Jedi would resort to it.
They’d just use a Force push. And can Vulcan leap as Jedi can?
Didn’t Dooku and Yoda try to fry eachother with force lightning in ep II? Last time I checked the little green fella was one of the good’uns.
And isn’t the plural of Jedi also Jedi?
Yoda just reflects the lightning back on Doku.
Current Expanded Universe canon - Jedi are fine (atm) with using Force lightning, as well as any other Sith power. Please don’t ask me to explain why, it’s all very complicated. Plus it reminds me of how the EU used to be…good. sighs
The Vulcan would attempt a mind meld on the Jedi, only to walk away shaking his head, saying, “These aren’t the droids we’re looking for.”
The Vulcan could just build a transporter, and beam the Jedi into a wall.
Well in order for them to battle they would have to exist within the same universe, in which case there are bound to be a number of force sensitive Vulcans among the Jedi ranks.
Which books-I’m a bit behind on my EU reading.
I know you were joking, but if the Vulcans had time to prepare they would probably win. They have a Higher Tech available and are more likely to devise workable plans to counter the greater mental abilities of the Jedis.
A few Vulcans might drop early but give them time to plan and reconfigure and I’ll bet on the Vulcans. Especially TOS & Next Gen Vulcan. I will continue to ignore the existence of Enterprise. 
JIm